One of the 57.5cm -long strings of an ordinary guitar is tuned to produce the no

Question

One of the 57.5cm -long strings of an ordinary guitar is tuned to produce the note B3(frequency 245 Hz) when vibrating in its fundamental mode.

A. Find the speed of transverse waves on this string

B. If the tension in this string is increased by 2.4% , what will be the new fundamental frequency of the string?

Express your answer using four significant figures.

C. If the speed of sound in the surrounding air is 344 m/s, find the frequency of the sound wave produced in the air by the vibration of the B3 string.

D. If the speed of sound in the surrounding air is 344 m/s, find the wavelength of the sound wave produced in the air by the vibration of the B3 string.

Explanation / Answer

A) f3 = 3V/2L

V = 2f3*L/3 = (2*245*0.575)/3 = 93.9167 m/s

B) T2 = T1+0.024T1 = 1.024T1

fo'/fo = sqrt(T2/T1) = sqrt(1.024)

fo'= 247.9226 Hz

C) f = 3V/2L = (3*344)/(2*0.575) = 897.3913 Hz

D) wavelength = V/f = 344/897.3913 = 0.3833 m

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